Estimating Network-Layer Topology Using End-to-End Measurements

ABSTRACT

A method for estimating the network-layer topology of a telecommunications network is described. In particular, the illustrative embodiment of the present invention estimates the existence and connectivity of nodes in the topology based on the detection of network-wide end-to-end path intersections. This is based on the assumption that pairs of streams of packets that share a common node will interfere and that the interference can be detected in the received streams. In general, this interference is manifested as jitter. By transmitting streams on each pair of end-to-end paths in the network, and detecting interference (or a lack of interference) a matrix of path intersections for the network can be created. Using logic and supposition, the topology of the network can be estimated using the matrix of path intersections. Once the estimate of the topology is complete, the maintenance and operation of the network can proceed based on the topology.

FIELD OF THE INVENTION

The present invention relates to telecommunications in general, and, more particularly, to the maintenance and operation of telecommunications networks.

BACKGROUND OF THE INVENTION

There are many situations in the maintenance and operation of a telecommunications network when it is useful to know the logical or network-layer topology of the network. In some cases, the network-layer topology of the network is known from those who constructed it, and in some other cases the network infrastructure can provide or determine the topology. In other cases, however, the network-layer topology is not known and must be estimated based on end-to-end measurements without the support of the network infrastructure. There are techniques in the prior art that attempt to do this, but they all exhibit limitations and disadvantages. Therefore, the need exists for a new method of estimating the network-layer topology of a network using end-to-end measurements.

SUMMARY OF THE INVENTION

The present invention provides a method for estimating the network-layer topology of a telecommunications network without some of the costs and disadvantages for doing so in the prior art. For example, the illustrative embodiment of the present invention estimates the existence and connectivity of nodes in the network based on the interference of streams of packets that traverse the network. When two streams of packets traverse two end-to-end paths in the network and one stream causes jitter in the other, it can be deduced that the two paths share a common node.

In accordance with the illustrative embodiment, each pair of streams is transmitted with a particular temporal pattern. The pattern of one stream—the interference stream—is designed to induce jitter in the streams with which it shares a network node (e.g., a queue, a processor, etc.). The pattern of the interference stream is also designed to induced jitter that is distinguishable from background jitter. The pattern of the second stream—the probe stream—is designed to capture jitter caused by the interference stream in such a way that it can be readily distinguished from background jitter. By transmitting an interference stream and a probe stream on each pair of end-to-end paths in the network, all of the end-to-end path intersections for the network can be created.

Using logic and supposition, the topology of the network can be estimated using the knowledge of which end-to-end paths intersect and which do not. The topology of the network can only be estimated and not conclusively deduced because networks with different network-layer topologies can yield the same combination of end-to-end path intersections. For many applications, however, an estimated topology, even if imperfect, is useful.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 depicts a schematic diagram of the illustrative embodiment of the present invention.

FIG. 2 depicts a flowchart of the salient tasks associated with the operation of the illustrative embodiment of the present invention.

FIG. 3 depicts a flowchart of the salient tasks associated with the operation of task 201.

FIG. 4 depicts a flowchart of the salient tasks associated with the operation of task 304.

FIG. 5 depicts a flowchart of the salient tasks associated with the operation of task 401.

FIG. 6 depicts a flowchart of the salient tasks associated with the operation of task 402.

FIG. 7 depicts a flowchart of the salient tasks associated with the operation of task 202.

FIG. 8 depicts a flowchart of the salient tasks associated with the operation of task 203.

FIG. 9 depicts a diagram of the probe pattern, which comprises 7 seconds of small packets with spacing of 5 ms.

FIG. 10 a depicts a diagram of periodic interference pattern.

FIG. 10 b depicts a diagram of aperiodic interference pattern.

FIG. 11 a depicts a plot of z_(i) versus tr_(i) without interference by a periodic interference pattern.

FIG. 11 b depicts a plot of z_(i) versus tr_(i) with interference by a periodic interference pattern.

DETAILED DESCRIPTION

FIG. 1 depicts a schematic diagram of the illustrative embodiment of the present invention. The illustrative embodiment comprises: packet network 101 and six nodes 102-1 through 102-6 connected to packet network 101.

Packet network 101 comprises hardware and software, in well-known fashion, and is capable of transporting a stream of packets from any node to any other node. It will be clear to those skilled in the art how to make and use packet network 101. In accordance with the illustrative embodiment, the network-layer topology of packet network 101 is not initially known to applications on nodes 101-1 through 101-6, but is estimated using the methodology described in detail below.

Each of nodes 102-1 through 102-6 comprises hardware and software to enable it to perform the functionality described below. In accordance with the illustrative embodiment, each of nodes 102-1 through 102-6 is identical, but it will be clear to those skilled in the art, after reading this disclosure, how to make and use alternative embodiments of the present invention in which some or all of the nodes are different. Although the illustrative embodiment comprises six nodes, it will be clear to those skilled in the art, after reading this disclosure, how to make and use alternative embodiments of the present invention that comprise any number of nodes.

FIG. 2 depicts a flowchart of the salient tasks associated with the operation of the illustrative embodiment of the present invention.

In task 201, the illustrative embodiment generates a path intersection matrix A for packet network 101. The path intersection matrix A represents the knowledge of which end-to-end paths in packet network 101 intersect and which do not. To populate the path intersection matrix A, the illustrative embodiment empirically tests every pair of end-to-end paths in packet network 101 to determine whether they intersect or not. The process of testing every pair of end-to-end paths in packet network 101 to determine whether they intersect or not is described in detail below and in the accompanying figures.

In accordance with the illustrative embodiment, the following notation is used. Packet network 101 is represented as a graph G=(V,E) where V is the set of nodes (routers and hosts) and E is the set of edges representing network-layer connectivity between the nodes on V. The set N⊂V are nodes 102-1 through 102-6. The set of directional end-to-end paths between nodes in N is represented as P. A path p is considered an end-to-end path if both of its end nodes are in N. The cardinality of P is |P|=|N|×(|N|−1). An end-to-end path from n_(i)εN to n_(j)εN is represented as p_(i,j), where p_(i,j)εP.

Path intersection matrix A has dimensions |P|×|P|. Each element A_(a,b,c,d)=1 if p_(a,b)εP and p_(c,d)εP intersect at the network layer, and A_(a,b,c,d)=0 otherwise. The populated path intersection matrix A for packet network 101 is depicted in Table 1.

TABLE 1 Path Intersection Matrix A for Packet Network 101 p_(1,2) p_(1,3) . . . p_(6,4) p_(6,5) p_(1,2) 1 1 . . . 0 0 p_(1,3) 1 1 . . . 0 0 . . . . . . . . . . . . . . . . . . p_(6,4) 0 0 . . . 1 1 p_(6,5) 0 0 . . . 0 1

Although the illustrative embodiment empirically tests every pair of end-to-end paths in packet network 101 to determine whether they intersect or not, it will be clear to those skilled in the art, after reading this disclosure, how to make and use alternative embodiments of the present invention which empirically tests fewer than every pair of end-to-end paths in packet network 101.

In task 202, the illustrative embodiment estimates the topology of packet network 101 based on the path intersection matrix A generated in task 201. The topology of packet network 101 can only be estimated and not conclusively deduced because multiple networks with different, albeit similar, topologies can yield the same path intersection matrix. For many applications, however, an estimated topology, even if imperfect, is useful. It will be clear to those skilled in the art what applications require perfect knowledge of the topology and what applications can function satisfactorily with imperfect knowledge. Task 202 is described in detail below and in the accompanying figures.

In task 203, the illustrative embodiment transmits one or more packets through packet network 101 and directs those packets to be re-directed to or away from one or more specific nodes based on the topology as estimated in task 202. As is well known to those skilled in the art, an estimate of the topology of packet network 101 is useful for many applications including, but not limited to:

-   -   i. transmitting one or more packets to transit specific nodes         and to avoid specific nodes for the purposes of fault avoidance,         and     -   ii. transmitting redundant one or more packets to transit         alternative paths and nodes, and     -   iii. transmitting one or more packets to transit nodes that are         “closer” than other nodes.         Task 203 is described in detail below and in the accompanying         figure.

Generating Path Intersection Matrix A—FIG. 3 depicts a flowchart of the salient tasks associated with the operation of task 201. The execution of tasks 301 through 306 generates the empirical data for one element in path intersection matrix A, and, therefore, tasks 301 through 306 are performed for each pair of paths in P.

In task 301, the illustrative embodiment transmits a stream of probe packets s_(a,b) in a probe pattern on path p_(a,b) FIG. 9 depicts a diagram of the probe pattern, which comprises one small packet every five milliseconds for a total of seven seconds. It will be clear to those skilled in the art, however, after reading this disclosure, how to make and use alternative embodiments of the present invention in which the probe pattern has any duration, packet size, packet number, and packet spacing.

In task 302, the illustrative embodiment transmits an interference stream of packets s_(c,d) in an interference pattern on path p_(c,d) at the same time that probe stream s_(a,b) is transmitted on path p_(a,b). The salient desirable characteristic of the interference stream s_(c,d) is that if it shares a network-layer node (e.g., queue, processor, etc.) with the probe stream s_(a,b), the interference stream should “interfere” with the probe stream by imparting a temporal pattern of jitter to the probe stream that corresponds to the interference pattern. In accordance with the illustrative embodiment, the interference pattern is characterized by a combination of a scalar k, which represents the number of bursts in the interference pattern, and a vector of k−1 inter-burst intervals.

FIG. 10 a depicts a diagram of the interference pattern, which comprises 6 bursts of 1500-byte packets transmitted back-to-back at a one second inter-burst interval. It will be clear to those skilled in the art, however, after reading this disclosure, how to make and use alternative embodiments of the present invention in which the interference pattern comprises any number of bursts of any length at any inter-burst interval, whether periodic as in FIG. 10 a or aperiodic as depicted in FIG. 10 b. Aperiodic interference patterns are advantageous over periodic interference patterns because they can be more easily distinguished from noise than periodic patterns.

In task 303, the illustrative embodiment receives the probe stream s_(a,b) at node n_(b) in well-known fashion, and records for each packet i its arrival time tr_(i).

In task 304, the illustrative embodiment detects the interference (or lack of interference) of the probe stream s_(a,b) as received at node n_(b) by the interference stream s_(c,d). This is described in detail below and in the accompanying figures.

In task 305, the illustrative embodiment deduces that paths p_(a,b) and p_(c,d) intersect when and only when the illustrative embodiment detects, in task 304, interference of the probe stream s_(a,b) by the interference stream s_(c,d).

In task 306, the illustrative embodiment populates element A_(a,b,c,d) of path intersection matrix A with a 1 when the illustrative embodiment deduces that paths p_(a,b) and p_(c,d) intersect in task 305 and with a 0 when the illustrative embodiment deduces that paths p_(a,b) and p_(c,d) do not intersect.

Although the illustrative embodiment empirically tests two pairs of end-to-end paths at a time, it will be clear to those skilled in the art, after reading this disclosure, how to empirically test a plurality of pairs of end-to-end paths using multiple probe streams and a single interference stream. Furthermore, it will be clear to those skilled in the art, after reading, this disclosure, how to empirically test a plurality of end-to-end paths using one or more probe streams and multiple, distinguishable interference streams.

Detect Interference of Probe Stream s_(a,b) by Interference Stream s_(c,d)—FIG. 4 depicts a flowchart of the salient tasks associated with the operation of task 304.

In task 401, the illustrative embodiment generates jitter pattern J_(a,b,c,d) based on probe stream s_(a,b) and interference stream s_(c,d). Jitter pattern J_(a,b,c,d) is a combination of a scalar m, which represents the number of groups found and a vector of m−1 inter-group intervals. This is described in detail below and in the accompanying figure.

In task 402, the illustrative embodiment compares jitter pattern J_(a,b,c,d) to the interference pattern. In accordance with the illustrative embodiment, the interference pattern is deemed to be detected when either: (1) mε{k−Δ, . . . , k, . . . , k+Δ}, wherein Δ is an integer, or (2) at least k−ψ of the k−1 inter-burst intervals temporally correspond to k−ψ of the m−1 inter-group intervals, wherein ψ is a positive integer. In accordance with the illustrative embodiment, Δ=1 and ψ=3, but it will be clear to those skilled in the art, after reading, this disclosure, how to make and use alternative embodiments of the present invention that have any value of Δ (e.g., Δ=0, 1, 2, 3, 4, 5, 10, etc.) and any value of ψ (e.g., ψ=1, 2, 3, 4, 5, 10, etc.). Task 402 is described in detail below and in the accompanying figure. It will be clear to those skilled in the art, however, after reading this disclosure, how to make and use alternative embodiments of the present invention that use another test for detecting interference of the probe stream by the interference stream.

Generate sitter Pattern J_(a,b,c,d)—FIG. 5 depicts a flowchart of the salient tasks associated with the operation of task 401.

In task 501, the illustrative embodiment identifies the temporally-shifted packets in the probe stream s_(a,b) by calculating the temporal shift z_(i) for each packet i in the probe stream transmitted by node n_(a) at time t_(si) and received node n_(b) at time tr_(i):

Z _(i)=(tr _(i) −tr _((i-1)))−(ts _(i) −ts _((i-1)))  (Eq. 1)

wherein ts_((i-1)) and tr_((i-1)) are the sending and receiving times of the i−1^(th) packet, respectively. When there is no interference caused by interference stream s_(c,d), a plot of z_(i) versus tr_(i) looks like that depicted in FIG. 11 a, but when there is interference, a plot of z_(i) versus tr_(i) looks something like that depicted in FIG. 11 b. In FIG. 11 b, the six groups of temporally-shifted packets, caused by the six periodic bursts in interference stream s_(c,d), respectively, are clearly visible and distinguishable from the unshifted packets. Quantitatively, however, packet i is only considered temporally shifted if it satisfies at least one of Tests 1 though 4 and either Test 5 or Test 6.

Test 1 is satisfied if:

z _(i) <Q ₁−2D  (Test 1)

where Q₁ is the first quartile (25^(th) percentile) of Z and D is the difference between the 90^(th) and 10^(th) percentiles of Z.

Test 2 is satisfied if:

z _(i) >Q ₃+2D  (Test 2)

where Q₃ is the third quartile (75^(th) percentile) of Z.

Test 3 is satisfied if:

z _(i) <Q ₁−1.5IQR  (Test 3)

where IQR=Q₃−Q₁.

Test 4 is satisfied if:

z _(i) >Q ₃+1.5IQR  (Test 4)

Test 5 is satisfied if z_(i) is less than the 10^(th) percentile of Z, and test 6 is satisfied if z_(i) is greater than the 90^(th) percentile of Z. It will be clear to those skilled in the art, after reading this disclosure, how to make and use alternative embodiments of the present invention that use other tests and combinations of tests for identifying the temporally-shifted packets.

In task 502, the illustrative embodiment groups the temporally-shifted packets that are within E seconds of one another into m groups, wherein E is a real number and m is a positive integer. In accordance with the illustrative embodiment, E=200 ms, but it will be clear to those skilled in the art, after reading this disclosure, how to make and use alternative embodiments of the present invention which use other values of E.

In task 503, the illustrative embodiment computes the m−1 inter-group intervals where the arrival time for each group equals the median arrival time for the packets in that group.

Compare fitter Pattern J_(a,b,c,d) to Interference Pattern—FIG. 6 depicts a flowchart of the salient tasks associated with the operation of task 402.

In task 601, the illustrative embodiment compares k (i.e., the number of bursts in the interference pattern) to m (i.e., the number of groups in jitter pattern J_(a,b,c,d)).

In task 602, the illustrative embodiment compares the k−1 inter-burst intervals to the m−1 inter-group intervals computed in task 401 to determine if at least k−3 inter-burst intervals temporally correspond to k−3 inter-group intervals.

Estimate Topology of Packet Network 101 Based on Path Intersection Matrix A—FIG. 7 depicts a flowchart of the salient tasks associated with the operation of task 202. The illustrative embodiment employs four deductions, two suppositions, and a rule of thumb to estimate the network-layer topology of packet network 101 based on path intersection matrix A. By considering all of these as simultaneous truths, an estimate of the topology of packet network 101 can be made using the data in path intersection matrix A. If the application of a deduction and a supposition creates an irreconcilable conflict, the deduction overrules the supposition. Absent evidence to the contrary, a supposition is considered correct.

In task 701, when path p_(a,b) and path p_(c,d) intersect, the illustrative embodiment deduces the existence of at least one common node n_(i) that is in both path p_(a,b) and path p_(c,d). The existence of the node might or might not have been made previously through the application of the deductions and suppositions.

In task 702, when path p_(a,b) and path p_(c,d) do not intersect, the illustrative embodiment deduces that path p_(a,b) and path p_(c,d) do not share a common node. The existence of the node might or might not have been made previously through the application of the deductions and suppositions.

In task 703, when both path p_(a,b) and path p_(a,c) intersect path p_(d,e), the illustrative embodiment supposes the existence of at least one common node n_(i) (in addition to node n_(b)) that is in both path p_(a,b) and path p_(a,c). Here too, the existence of the node might or might not have been made previously through the application of the deductions and suppositions.

In task 704, when both path p_(a,b) and path p_(c,b) intersect path p_(d,e), the illustrative embodiment supposes the existence of at least one common node n_(i) (in addition to node n_(b)) that is in both path p_(a,b) and path p_(c,b). Here too, the existence of the node might or might not have been made previously through the application of the deductions and suppositions to other data.

In task 705, when (1) path p_(a,b) and path p_(d,e) intersect at a common node n_(i), and (2) path p_(a,c) does not intersect path p_(d,e), the illustrative embodiment deduces that path p_(a,c) does not comprise node n_(i). This deduction is useful to rebut a supposition made in either task 703 or 704.

In task 706, when (1) path p_(a,b) and path p_(d,e) intersect at a common node n_(i), and (2) path p_(c,b) does not intersect path p_(d,e), the illustrative embodiment deduces that path p_(c,b) does not comprise node n_(i). This deduction is useful to rebut a supposition made in either task 703 or 704.

Additionally, a rule of thumb applies when two paths originate or terminate at a single node. The larger the number of paths that both paths intersect (and fail to intersect), the longer the segment (i.e., edges and nodes) shared by the two paths. This can be determined by assessing the similarity between the two column vectors in the path intersection matrix that correspond to the two paths. In other words, if two paths originate or terminate at a single node, a low Hamming distance between the two column vectors for those paths suggests a long shared segment between the paths.

It will be clear to those skilled in the art, after reading this disclosure, how to estimate the topology of any network based on these deductions, suppositions, and the rule of thumb.

Utilize Deduced Topology of Packet Network 101 to Route Packets—FIG. 8 depicts a flowchart of the salient tasks associated with the operation of task 203.

In task 801, the illustrative embodiment transmits a packet or stream of packets to:

-   -   (a) transit a first node n₁ and not transit a second node n₂ in         some circumstances (e.g., when the jitter pattern corresponds to         the temporal pattern, etc.); and     -   (b) transit the second node n₂ and not transit the first node n₁         in some other circumstances (e.g., when the jitter pattern fails         to correspond to the temporal pattern, etc.).

In task 802, the illustrative embodiment transmits a packet or stream of packets to:

-   -   (a) transit both a first node n₁ and a second node n₂ in some         circumstances (e.g., when the jitter pattern corresponds to the         temporal pattern, etc.); and     -   (b) transit neither second node n₂ nor the first node n₁ in some         other circumstances (e.g., when the jitter pattern fails to         correspond to the temporal pattern, etc.).

It is to be understood that the disclosure teaches just one example of the illustrative embodiment and that many variations of the invention can easily be devised by those skilled in the art after reading this disclosure and that the scope of the present invention is to be determined by the following claims. 

1. A method comprising: detecting interference by a first stream of packets on a second stream of packets in a packet network, wherein the second stream of packets is transmitted from a first node n₁ to a second node n₂ via a first path p_(1,2) in the packet network; detecting interference by the first stream of packets on a third stream of packets in the packet network, wherein the third stream of packets is transmitted from the first node n₁ to a third node n₃ via a second path p_(1,3) in the packet network; deducing that both the first path p_(1,2) and the second path p_(1,3) comprise a fourth node n₄ because both the second stream of packets and the third stream of packets are interfered by the first stream of packets; and transmitting a packet to transit the fourth node n₄.
 2. The method of claim 1 further comprising: detecting no interference by the first stream of packets on a fourth stream of packets in the packet network, wherein the fourth stream of packets is transmitted from the first node n₁ to a fifth node n₅ via a third path p_(1,5) in the packet network; deducing that the third path p_(1,5) comprises a sixth node n₆ that is not in the first path p_(1,2) or the second path p_(1,3) because the fourth stream of packets is not interfered by the first stream of packets; and transmitting a second packet to transit the sixth node n₆.
 3. A method comprising: detecting interference by a first stream of packets on a second stream of packets in a packet network, wherein the second stream of packets is transmitted from a first node n₁ to a second node n₂ via a first path p_(1,2) in the packet network; detecting interference by the first stream of packets on a third stream of packets in the packet network, wherein the third stream of packets is transmitted from a third node n₃ to the second node n₂ via a second path p_(3,2) in the packet network; deducing that both the first path p_(1,2) and the second path p_(3,2) comprise a fourth node n₄ because both the second stream of packets and the third stream of packets are interfered by the first stream of packets; and transmitting a first packet to transit the fourth node n₄.
 4. The method of claim 3 further comprising: detecting no interference by the first stream of packets on a fourth stream of packets in the packet network, wherein the fourth stream of packets is transmitted from a fifth node n₅ to the second node n₂ via a third path p_(5,2) in the packet network; deducing that the third path p_(5,2) comprises a sixth node n₆ that is not in the first path p_(1,2) or the second path p_(3,2) because the fourth stream of packets is not interfered by the first stream of packets; and transmitting a second packet to transit the sixth node n₆.
 5. A method comprising: detecting interference by a first stream of packets on a second stream of packets in a packet network, wherein the second stream of packets is transmitted from a first node n₁ to a second node n₂ via a first path p_(1,2) in the packet network; detecting no interference by the first stream of packets on a third stream of packets in the packet network, wherein the third stream of packets is transmitted from the first node n₁ to a third node n₃ via a second path p_(1,3) in the packet network; deducing that the first path p_(1,2) comprises a fourth node n₄ and that the second path p_(1,3) does not comprise the fourth node n₄ because the second stream of packets is interfered by the first stream of packets but the third stream of packets is not interfered by the first stream of packets; and transmitting a first packet to transit the fourth node n₄.
 6. A method comprising: detecting interference by a first stream of packets on a second stream of packets in a packet network, wherein the second stream of packets is transmitted from a first node n₁ to a second node n₂ via a first path p_(1,2) in the packet network; detecting no interference by the first stream of packets on a third stream of packets in the packet network, wherein the third stream of packets is transmitted from a third node n₃ to the second node n₂ via a second path p_(3,2) in the packet network; deducing that the first path p_(1,2) comprises a fourth node n₄ and that the second path p_(3,2) does not comprise the fourth node n₄ because the second stream of packets is interfered by the first stream of packets but the third stream of packets is not interfered by the first stream of packets; and transmitting a first packet to transit the fourth node n₄. 